### view libtommath/bn_mp_montgomery_reduce.c @ 1436:60fc6476e044

Update to libtommath v1.0
author Matt Johnston Sat, 24 Jun 2017 22:37:14 +0800 5ff8218bcee9 8bba51a55704
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```#include <tommath_private.h>
#ifdef BN_MP_MONTGOMERY_REDUCE_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
*
* LibTomMath is a library that provides multiple-precision
* integer arithmetic as well as number theoretic functionality.
*
* The library was designed directly after the MPI library by
* Michael Fromberger but has been written from scratch with
* additional optimizations in place.
*
* The library is free for all purposes without any express
* guarantee it works.
*
* Tom St Denis, [email protected], http://libtom.org
*/

/* computes xR**-1 == x (mod N) via Montgomery Reduction */
int
mp_montgomery_reduce (mp_int * x, mp_int * n, mp_digit rho)
{
int     ix, res, digs;
mp_digit mu;

/* can the fast reduction [comba] method be used?
*
* Note that unlike in mul you're safely allowed *less*
* than the available columns [255 per default] since carries
* are fixed up in the inner loop.
*/
digs = (n->used * 2) + 1;
if ((digs < MP_WARRAY) &&
(n->used <
(1 << ((CHAR_BIT * sizeof(mp_word)) - (2 * DIGIT_BIT))))) {
return fast_mp_montgomery_reduce (x, n, rho);
}

/* grow the input as required */
if (x->alloc < digs) {
if ((res = mp_grow (x, digs)) != MP_OKAY) {
return res;
}
}
x->used = digs;

for (ix = 0; ix < n->used; ix++) {
/* mu = ai * rho mod b
*
* The value of rho must be precalculated via
* montgomery_setup() such that
* it equals -1/n0 mod b this allows the
* following inner loop to reduce the
* input one digit at a time
*/
mu = (mp_digit) (((mp_word)x->dp[ix] * (mp_word)rho) & MP_MASK);

/* a = a + mu * m * b**i */
{
int iy;
mp_digit *tmpn, *tmpx, u;
mp_word r;

/* alias for digits of the modulus */
tmpn = n->dp;

/* alias for the digits of x [the input] */
tmpx = x->dp + ix;

/* set the carry to zero */
u = 0;

/* Multiply and add in place */
for (iy = 0; iy < n->used; iy++) {
/* compute product and sum */
r       = ((mp_word)mu * (mp_word)*tmpn++) +
(mp_word) u + (mp_word) *tmpx;

/* get carry */
u       = (mp_digit)(r >> ((mp_word) DIGIT_BIT));

/* fix digit */
*tmpx++ = (mp_digit)(r & ((mp_word) MP_MASK));
}
/* At this point the ix'th digit of x should be zero */

/* propagate carries upwards as required*/
while (u != 0) {
*tmpx   += u;
u        = *tmpx >> DIGIT_BIT;
*tmpx++ &= MP_MASK;
}
}
}

/* at this point the n.used'th least
* significant digits of x are all zero
* which means we can shift x to the
* right by n.used digits and the
* residue is unchanged.
*/

/* x = x/b**n.used */
mp_clamp(x);
mp_rshd (x, n->used);

/* if x >= n then x = x - n */
if (mp_cmp_mag (x, n) != MP_LT) {
return s_mp_sub (x, n, x);
}

return MP_OKAY;
}
#endif

/* \$Source\$ */
/* \$Revision\$ */
/* \$Date\$ */
```